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f(2) = 2² + k (2) + c = 0 f(-3) = -3² + k (-3) + c = 35 Drop the functions on the left and multiply...4 - 12 + 8 = 0 9 + 18 + 8 = 35 -8 + 8 = 0 27 + 8 = 35 0 = 0 35 = 35 This checks. k = -6 and c = 8

C = k / (m(1 - k )) cross multiply Cm(1 - k ) = k distribute LHS Cm - Cmk = k add Cmk to both sides Cm = k + Cmk factor Cm = k (1 + Cm) divide both sides by (1...

Do you mean y = asin[ k (x - c )] + d? y = asin[ k (x - c )] + d Subtract both sides by d: y...d)/a)/ k Finally, add both sides by c : x = arcsin((y - d)/a)/ k + c I hope this helps!

See binomial equation [1 + x]^n = C (n,0)+ x* C (n,1) +(x^2)* C (n,2)+ (x^3)* C (n,3) ... + [x^n-1...(n,1)+ (2*x)* C (n,2) + (3x^2)* C (n,3)+ ... + (n-1)*[x^n-2]⋅ C (n,n-1) + n*[x^n-1]* C (n,n) put x = 1, you will see that right part is...

...black is given by the well-known hyper-geometric formula: P( k ) = C [M, k ] * C [(N-M),(n- k )] / C [N,n], /numerator...

... in the formula: since k = n - (n- k ), we have: C (n, k ) = n! / ( k ! (n- k )! ) C (n, n- k ) = n! / ((n- k )! (n - (n- k ))! = n! / ( (n- k )! k ! )

Since the series includes the term (x- c )^ k we know the power series expresses a function of x "centered at...all over |a_ k (x- c )^ k | is less than 1. So... lim k »∞ | a_( k +1)(x- c )^( k +1) / [a_ k (x- c )^ k ] | < 1 Since (x- c )^( k +1)/(x- c )^ k can...

...1 Now put x = 1 and you will get ......................n n*(2)^(n - 1) = ∑ k * C (n, k ) ................... k =1